The resisters in escape lines didn’t put any effort into naming themselves. They weren’t planning any big advertising campaigns or even registering themselves with the authorities. They most definitely didn’t want the authorities to know they existed. They wanted to stay under the radar.

Nonetheless, they must at some point have needed to refer to their own network among themselves. In Dutch-Paris, some of the resisters called themselves the “pastor’s network”. That was either after a pastor in Brussels who was one of the leaders of the Comité there, or the pastor in Geneva who channeled funds to the rescue efforts and ran the illegal exchange of information between the Dutch resistance and the Dutch government-in-exile. Either way, the “pastor’s line” was only used by the few people who worked with either pastor. A few resisters called it the “Oranjelijn” in a patriotic nod to the Dutch royal house of Oranje, because it was a Dutch line. But most of the people in the line were not Dutch and not overtly loyal to Queen Wilhelmina. Most members of Dutch-Paris just called it “the organization,” if they called it anything at all.

So if the resisters didn’t give their own networks their names, who did? The Allied military did. The American and British governments were officially interested in any civilian who offered help to American and British soldiers and aviators in occupied territory. During the war, they put a fair amount of effort into teaching their air crews escape and evasion tactics, which included finding helpful civilians and following those resisters’ instructions. They also felt an obligation to help those civilians who were putting themselves and their families at risk to help evading servicemen.
The British created a unit called MI-9 to encourage evasion. The Americans called their unit MIS-X. Naturally, as military bureaucracies, they embarked on making reports, maps, charts etc etc.

They interviewed all personnel who came out of occupied Europe about the reasons their aircraft crashed, what happened on the ground, who helped them, what the helpers looked like, where they lived, where they hid the men and took the men. They pieced the puzzle of resistance networks together as best they could (which was fair to middling). And they gave the networks names.
In the case of Dutch-Paris, one of the aviators asked a Dutch-Paris guide what the name of the network was while standing in a train station in Paris. The resister didn’t have an answer, but a train station full of German and French police was not the place to get into a long discussion of resistance safety protocols. So he said “Dutch-Paris” because as far as he was concerned it was a Dutch group and it went through Paris. He was speaking English, which is why this Dutch-Belgian-French network has an English name.

The aviator made it to Spain and back to England. When he gave his report, he said that he was taken to Spain by Dutch-Paris. The officers debriefing him seized on the name, collated the details and started using the name in reports. At the liberation, they moved their operations to Paris and Brussels. By that time Jean Weidner, the acknowledged leader of Dutch-Paris, had been commissioned as a Captain in the Dutch Army and put in charge of the Netherlands Security Service in Paris. He was savvy enough to know that it would be a lot easier to get the recognition and assistance that his resistance colleagues deserved for them if he went with the name that the British and Americans were already using. Plus, he didn’t have another name for the network or any way of getting all 300+ members of the line together to decide one.

Having an official name made it possible for Weidner to establish the network as an official resistance organization in France, Belgium and the Netherlands. It made a lot of paperwork easier for a lot of people. And it made it easier for journalists to write about Dutch-Paris. Smaller escape lines that didn’t have official names recognized by the Allies and/or savvy leaders in powerful positions ended up as sub-groups of other networks just because that’s the way the bureaucrats decided to organize their files.

The legendary Comet escape line, incidentally, got its name because British diplomats in Spain needed to call it something. Comet seemed fitting because fugitives got from Belgium to Spain so quickly under their care, at the speed of a comet.